Market and underground activities in a two-sector dynamic equilibrium model

Summary. In this paper a two sector dynamic general equilibrium model is developed in order to evaluate the implications of the underground economy from a business cycle perspective. There are three main results. First, introducing an underground sector improves the fit of the model to the data, especially along several important labor market dimensions. Second, the model produces substantial internal propagation of temporary shocks. Third, it is shown that underground activities offer risk sharing opportunities by allowing households to smooth income through a proper labor allocation between the two sectors.Received: 17 June 2002, Revised: 25 April 2003, JEL Classification Numbers: E320, E260, J22, H200.We have benefited from the comments and suggestions of John Donaldson. We would also like to thank Paolo Siconolfi, Jean Pierre Danthine, Fausto Gozzi, Edmund Phelps, Gustavo Piga, Domenico Tosato, and the participants in the seminars at various universities, David Giles and Stefano Pisani for providing useful information on the underground data, Francesca Caponi for the comments and the information concerning the legal and fiscal aspects involved in the calibration, and Glenn Williams for the research assistance. Finally, we thank two anonymous referees for helpful comments on this and on earlier versions of the paper. Chiarini acknowledges financial support from the Ateneo Research fund of the University of Rome, La Sapienza, Dinamiche dell'integrazione europea e scelta di politica economica. All errors are ours. Correspondence to: F. Busato     

Effect of restricting asset trade in dynamic equilibrium models

Abstract. This paper shows that differences between the predictions of an international real business cycle model with complete markets and the predictions of a model where agents can trade only risk-free bonds depend heavily on three parameters: discount factor, and degrees of persistence and spillovers in productivity shocks. This sensitivity explains apparently paradoxical results previously obtained in the literature. Also, since empirical work finds that two of those parameters are not estimated precisely, the outcomes of quantitative studies comparing complete-markets and bond economies using only the point estimates of those parameters inherit the substantial uncertainty in the parameter estimates.     

Potential economic reforms in North Korea: a dynamic general equilibrium model

We use a dynamic general equilibrium model to examine hypothetical market reforms in North Korea. We model partial reform, in which producers choose capital allocations across sectors, with the government still fixing total capital. We also consider two full market reform scenarios. In one, public infrastructure investment remains unchanged, while, in the other, it increases substantially. In all scenarios, we assume a closed economy and a constant military size. Our simulations show little hope for the North Korean economy without boosting infrastructure. Although all of the reforms raise consumption, only significant increases in infrastructure investment bring positive economic growth.     

Stability, global dynamics and Markov equilibrium in models of endogenous economic growth

This paper studies the local and global dynamics of two-sector models of endogenous growth with economy-wide external effects and taxes on capital and labor. The local analysis classifies the parameter space depending on the number of stationary solutions and local stability of equilibria. The global analysis shows that if taxes are within certain bounds and the size of the external effects on the average level of human capital is smaller than the share of physical capital, the equilibrium path is monotone and therefore a continuous Markov equilibrium can be constructed.     

Non-computability of competitive equilibrium

Summary. We provide a “computable counterexample” to the Arrow-Debreu competitive equilibrium existence theorem [2]. In particular, we find an exchange economy in which all components are (Turing) computable, but in which no competitive equilibrium is computable. This result can be interpreted as an impossibility result in both computability-bounded rationality (cf. Binmore [5], Richter and Wong [35]) and computational economics (cf. Scarf [39]). To prove the theorem, we establish a “computable counterexample” to Brouwer's Fixed Point Theorem (similar to Orevkov [32]) and a computable analogue of a characterization of excess demand functions (cf. Mas-Colell [26], Geanakoplos [16], Wong [50]). Received: September 9, 1997; revised version: December 17, 1997     

Learning competitive equilibrium in laboratory exchange economies

A laboratory market for two goods is instituted to examine the hypothesis that individuals will eventually coordinate on the induced competitive equilibrium. The mechanism for exchange strongly restricts the space of agent actions, facilitating the identification of decision rules. Evidence for learning competitive equilibrium is mixed due to strong heterogeneity in decision making. Some subjects forego immediately available gains when they expect the market to move in a more favorable direction, a condition necessary for coordinating on the competitive outcome. However, a majority do not, and many are content to satisfice, though the means to do better was reasonably transparent. I gratefully acknowledge the advice and tutelage of John Duffy and Stephen Spear, and would also like to thank David Grether, Dan Houser, Michael Peress, Bryan Routledge, Shyam Sunder, and participants at the Midwest Theory meetings (Bloomington) and the ESA regional meetings (Tucson) for useful feedback. Two patient and insightful anonymous referees have helped to greatly improve this paper and my future written endeavors. This project was financially supported by the Department of Economics at Carnegie Mellon University, the International Foundation for Research in Experimental Economics at George Mason University, and the Social and Information Sciences Laboratory at Caltech, as well as by Stephen Spear. Finally, special thanks is owed to Allen Geary, Jr. for co-developing the software used in these experiments, and to the Pittsburgh Experimental Economics Laboratory for use of its facilities.     

On the uniqueness of competitive equilibrium

Summary . The paper is concerned with the following question: in addition to local uniqueness, what other conditions must be imposed to ensure global uniqueness of competitive equilibrium? The answer is provided within a standard framework involving excess demand functions. Conditions are identified which have the nice property that they are true close to a regular equilibrium. Uniqueness is established by considering an adjustment process and showing that under the mentioned conditions, every equilibrium is locally asymptotically stable and moreover the process itself is globally stable; uniqueness follows from an Arrow and Hahn (1971) result. Alternatively, the paper may be seen as identifying conditions under which there is a vectorfield satisfying the requirements of an uniqueness result due to Dierker (1974). Received: July 1, 1996; revised version October 7, 1996     

Unhedgeable shocks and statistical economic equilibrium

We develop a statistical concept of economic equilibrium as the stationary distribution of a random walk on the exchange equilibrium set (the contract set) of a pure exchange economy induced by unhedgeable shocks that perturb the economy from the exchange equilibrium set and subsequent disequilibrium trading that returns the economy to a new equilibrium. The Fokker–Planck equation for the resulting drift-diffusion process implies that the stationary distribution is independent of the size of the shock so that a small-disturbance limiting distribution is well defined. We present explicit solutions for the statistical equilibrium for the cases of quasilinear and Gorman-aggregatable Cobb–Douglas economies, and illustrate the results in the context of a generic dividend-discount model to emphasize the distinction between insurable risk and unhedgeable uncertainty in this context. The statistical equilibrium of income or wealth for quasilinear economies is described by an exponential Gibbs distribution. The statistical equilibrium income and wealth distributions for Gorman-aggregatable Cobb–Douglas economies can take a wider variety of forms, including power-law and gamma distributions. The statistical equilibria calculated for these examples suggest a close relation to widely observed statistical distributional regularities in real-world economies.     

Von neumann facets and the dynamic stability of perfect foresight equilibrium paths in neo-classical trade models

I am grateful to two anonymous referees for useful comments on an earlier version of this paper.     

Unemployment equilibrium and economic policy in mixed markets

This paper features a simple static Cournot-Nash model of an exchange economy with two productive sectors at flexible prices and wages. The traders in the atomless sector are price-takers, while the atoms behave strategically. We focus on the consequences of strategic interactions on the market outcome. Firstly, strategic interactions create underemployment on the labor market. Secondly, when the number of atoms increases without limit, the CWE coincides with the competitive equilibrium. Thirdly, we compare the welfare reached by traders at both equilibria. Fourthly, we consider the implementation of a tax levied on strategic supplies. Finally, we compare the approach retained with the monopolistic competition framework.     

A competitive equilibrium for a warm-glow economy

The warm-glow model (Andreoni in J Political Econ 97:1447–1458, 1989; Econ J 100:464–477, 1990) of public goods provision has received widespread interest, yet surprisingly most attention has focused on the voluntary contribution equilibrium of the model, and only very little attention has been devoted to the competitive equilibrium. In this paper, we introduce the concept of competitive equilibrium for a warm-glow economy (henceforth, warm-glow equilibrium) and establish both existence and welfare properties. The warm-glow equilibrium concept may prove to be very useful to the normative and positive theory of public goods provision. First, it is a price-based mechanism achieving efficient outcomes. Second, not only could the warm-glow equilibria outcomes serve as a point of reference to measure free-riding and welfare loss but also, as suggested by Bernheim and Rangel (Behavioral Economics and Its Applications, 2007), in large economies they may be approximated by Walrasian equilibria outcomes.     

A general equilibrium framework for the affine class of term structure models

The Duffie and Kan (1966) model, which can be considered as the most general affine term structure formulation, was originally specified in terms of risk-adjusted stochastic processes for its state variables. The goal of the present paper is to derive a Duffie and Kan (1966) model specification under the physical probability measure that is compatible with the formulation given by the authors under the equivalent martingale (money market account) measure. For that purpose, the Duffie and Kan (1966) model will be fitted into a general equilibrium monetary framework. The resulting analytical solution for the vector of factor risk premiums enables the econometric estimation of the model parameters using a time-series or a panel-data approach, and nests, as special cases, several other specifications already proposed in the literature.Received: November 2002, Accepted: February 2004, JEL Classification: E43, G11, G12Financial support by FCTs research grant PRAXISXXI/BD/5712/95 is gratefully acknowledged.     

Constant returns to scale and competitive equilibrium under uncertainty

This paper considers the implications of the assumption of constant returns to scale in expected utility maximizing models of the competitive firm or industry in which markets for risk are absent. Under widely used assumptions about risk preferences it is shown that with constant returns to scale average profits are more than necessary to cover the implicit costs of risk-bearing. When the free entry of identical firms is possible this assumption about technology is shown to be incompatible with the assumption that entrepreneurs are risk averse.     

Proper belief revision and equilibrium in dynamic games

We present a theory of rationality in dynamic games in which players, during the course of the game, may revise their beliefs about the opponents’ utility functions. The theory is based upon the following three principles: (1) the players’ initial beliefs about the opponents’ utilities should agree on some profile u of utility functions, (2) every player should believe, at each of his information sets, that his opponents are carrying out optimal strategies and (3) a player at information set h should not change his belief about an opponent's ranking of strategies a and b if both a and b could have led to h. Scenarios with these properties are called preference conjecture equilibria for the profile u of utility functions. We show that every normal form proper equilibrium for u induces a preference conjecture equilibrium for u, thus implying existence of preference conjecture equilibrium.     

Market institutions and economic evolution

Our cognitive limitations cause us to rely on institutions to guide reasonable behaviour; market institutions reduce the costs of search, negotiation, and monitoring entailed in making single transactions. The making of markets requires an investment of immaterial capital, the major share of which typically is provided by those who expect to be very active on one side of the market. This `external organisation' provides producers with information for the development of new products; by simplifying transactions it also allows consumers greater scope for developing consumption capabilities. Thus the evolution of institutions guides the evolution of goods and services.     

Selecting a unique competitive equilibrium with default penalties

The enlargement of the general-equilibrium structure to allow for default subject to penalties results in a construction of a simple mechanism for selecting a unique competitive equilibrium. We consider economies for which a common credit money can be applied to uniquely select each of the competitive equilibria with suitable default penalties. We identify two classes of such economies.     

Introduction to dynamic general equilibrium

This introduces the symposium on dynamic general equilibrium.